The former captain had been due to join the team on their limited-overs tour of West Indies beginning on Friday but he quit on Tuesday after revealing a breakdown in his relationship with Kohli, who was said to resent his assertive coaching style.
"(He) has expressed his views and taken a decision to step out. We all respect that decision," Kohli told reporters in Port-of-Spain, Trinidad on the eve of the first one-day international against West Indies.
Kumble said in a message that he was surprised when the Indian board told him of Kohli's reservations concerning his 'style' and his plans to continue as head coach of the team.
Queried about the circumstances that led to Kumble's exit, the India captain was predictably reticent, citing the sanctity of the dressing room for his silence on the issue.
"We have created a culture over the last three-four years that whatever happens in the changing room, we've tried to maintain the sanctity of the changing room throughout," he said.
"...what happens in the changing room is something that's very sacred and private to all of us, and something that I would not express in details in a public scenario.
"As I said, his point of view is out there and we respect that decision."
Kumble's exit has been perceived at home as a victory for player power, which will also send out the wrong signal to whoever succeeds the former spin bowler in the high-profile job.
"I have total respect for him as a cricketer and what he has achieved for the nation, all the years that he has played," Kohli added. "There's no taking away that aspect of him at all. And we all respect him totally."
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
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